# Wikipedia:WikiProject Numbers

This WikiProject is aimed at standardizing the pages on numbers. Although most of the articles on numbers currently follow a format, they do so to varying degrees. A template is given below based on the general tendencies of the number articles so far. Once the template has been examined and optimized, then the work will begin of converting each number article to conform.

## Guidelines

### How far to go?

There is no need to remind anyone here that there are infinitely many numbers, for we all already know that. Despite what some may rant, no one here has any intention of making a robot to make number articles. All number articles will be written by humans, because we want to have articles on numbers that humans might want to look up; thus the articles will take into account the humanistic qualities of numbers. So the question is, what numbers should there be articles for?

• Integers: Continuous from −1 to 200. Multiples of 100 from 300 to 900, then multiples of 1000 to 9000. Afterwards, only powers of 10 (from 1 up to 1012, higher than that only if they have a standard word name and commonly used SI prefix) and numbers with some remarkable mathematical property.
• Fractions: Fractions from halves (1/2) to twentieths (1/20 to 19/20) are acceptable at this point. Fractions that are in common use and have a code point assigned in the Unicode Number Forms block can use articles as well. (Composed characters don't count). Redirections for equivalent fractions need to be created.
• Reals: Important mathematical constants such as e and π.
• Imaginaries: At the very least, i
• Non-numerical entities: NaN, with a possible redirect from Not a Number
• Number bases: Those that are actually used (or have been used in the past) for practical calculations, such as binary, octal, decimal, hexadecimal, vigesimal, and sexagesimal.

#### Creating a new article or adding onto an existing one

Care should be taken to only create a new article on a number if there is sufficient known information to create an article that consists of more than just "N comes after N - 1 and before N + 1". As a guideline, you ought to know at least three interesting properties of a number. What constitutes interesting can be debated (see Wikipedia:Evaluating how interesting an integer's mathematical property is for one possible way of gauging this), but the point is that the careless creation of number article stubs is to be avoided. Also, and as importantly in many respects, which cultural and scientific properties (or otherwise) can be attributed to the number? For a complete number article, there need-be at least one accompanying important cultural association aside from mathematical properties present. If you only know one interesting mathematical property, consider jotting it down in an article on a near round number. For instance, if you want to write an article on 1050, see if something about it has already been written on it at 1000. That's the point of the series of stubs at the ends of articles like 500 and 7000, to see if there are numbers outside the declared project range that might merit their own article.

So, before creating a new article on a number, go over a checklist:

1. See if the number has already been written about at an article on a near round number (rounding down, i.e. if searching for the number 455, seek the page 400).
2. Name at least three interesting and unrelated mathematical properties of the number (or one earth-shatteringly interesting property, such as odd perfect number, or a quasiperfect number of either parity).
3. Fill out a Docuan table (see below) with the basic properties of the number (factorization, binary representation, etc.)
4. Understand whether other fields have associations with the number, so as to include whichever philosophical, cultural and scientific links that are relevant.
5. Follow the template below once you have sufficient information to start a new article, or add onto an existing one.

### Template for integers

#### Outline of template

Each article on a number ought to consist of two major sections, the first dealing with the mathematical properties of the number, the second dealing with the extramathematical properties of the number, such as cultural associations of the number.

1. Mathematical properties
1. Representation (decimal, Roman, Mayan, hexadecimal, etc.)
2. Arithmetic, number theory properties
3. Algebraic properties
4. Calculus properties
5. Geometric properties
2. Extra-mathematical properties
1. Most universal and eternal
2. Most local and ephemeral still worth listing.

This template (originally developed by Docu) is a subtractive template; i.e. given a number N that has all relevant mathematical properties (even mutually exclusive ones), including extra-mathematical properties. To use this template, replace the in-line generic statements with appropriate information:

N (number)

N (digit 10's place of number N-digit 1's place of number N) is the natural number following N - 1 and preceding N + 1. It is mainly known culturally (or in mathematics) for X and Y reason.

In mathematics

Number N
CardinalN
OrdinalNth
Numeral systemN-cimal or N-ary
Factorization(prime number) or px ... py
Roman numeralN
BinaryN2

N is the Xth prime number, the previous being N - 2x, with which it comprises a twin (or cousin, sexy) prime. It is also a Mersenne prime (or a a Fermat prime, a permutable prime, a palindromic prime, a composite number, a highly composite number, an abundant number, a surreal number, and an amicable number with ...)

It is the sum of n-consecutive primes, (px + px+1 + px+2...)

N has a Euler totient value of X.

It a polygonal number, and the square of x. It occurs in the X-sequence, and is an Y-type number.

In normal space, the interior or exterior angles of a X-agon measure N degrees each.

(Note: there should be links to the relevant articles (which already contain lists of that kind of number). There's little point in creating, say, a category of Mersenne primes; especially since most Mersenne primes won't ever have their own article.)

In other fields

N is also:

• The atomic number of elementium.
• The Messier Number of Object A
• The NGC (New General Catalog) Number of Object A
• The Saros Number of a solar (or lunar) eclipse series.
• Considered lucky/unlucky in Country A.
• Very important in Religion A's sacred texts. (* Better to let Wikipedians versed in theology decide which religious associations of a number ought to be included *)
• The designation of Country A's Highway Route Number N, which runs from Point A to Point B. (* Only major highways need be included, unless they have achieved fame beyond their location. *)
• The code for international direct dial phone calls to Country A.
• The registry number of the USS/HMS/RMS ShipName, CVN-Number N. (* Only major ships, such as aircraft carriers and gigantic cruise liners need be included. *)
• In the expression "folksy expression with Number N".
• In the title of the movie There's Something About Number N. (* Only major studio releases ought to be included. Include independent releases if they achieve fame comparable to a major studio release. *)
• In sport, the retired jersey number of legendary player Babe McGwire.

References

• Pencil, Sharp (January 2004). "Integers". Encyclopedia of Things. Open Publishing. Retrieved 2021-01-01.
• Eraser, Smooth (January 2022). "Constants". Encyclopedia of Things. Open Publishing. Retrieved 2023-01-01.

### Cultural associations

It is preferable to have a stub article than to pad an article with trivial or tenuously related information. Normal Wikipedia policies and guidelines should be considered when choosing what content to include in a number article. Specifically, any cultural associations of a number must be significant, verifiable, and covered with due weight. See the essay Wikipedia:"In popular culture" content for guidance on how to select appropriate cultural references.

Remember that the subject of the article is the number (the mathematical object), not the string of characters commonly used to represent the number. Take care to include only significant cultural associations of the number. Do not include content that relates to the article's title only as an identifier, or label, or simple enumeration, or measurement, or as a trivial mention. For example:

• Route 66 does not have a significant relationship with the number 66 - rather, the "66" is an identification code.
• 86 (novel series) is not about the number 86.
• The 35 in 35 mm film is a measurement, not a property of, or reference to, the number 35.
• The 9 in ISO 9 is a simple enumeration of a series of items, with no significant relationship with the number 9.
• The centre-forward in association football wearing the number 9 shirt is a trivial mention of the number 9.

If there is plausible ambiguity between such items and the given string of characters, the place to mention it would be on a disambiguation page for the number.

### Citations

Just as with any information in Wikipedia, articles on numbers need to cite sources. (See Wikipedia:Citing sources for general information on citing sources).

Some statements that are easily verified with a pocket calculator might not need citations (e.g., the fact that 73 = 343), but anything slightly more difficult to verify does (e.g., that 786 might be the largest number for which 2nCn is not divisible by the square of an odd prime).

It is not the place of this project to prescribe a citation format. Until Wikipedia decides on a uniform citation format, number articles may use whatever citation format would be acceptable in a mathematics journal

The OEIS and Mathworld are respectable Web sources, as are Web versions of respected professional journals.

It is acceptable for a number article to have few citations if the linked 'word' articles have primary and secondary sourcing.

### Edit summaries

Every project member (indeed anyone who edits Wikipedia) is encouraged to write brief but complete edit summaries. (See Wikipedia:Edit summary for advice on writing edit summaries for articles on any topic).

For articles about numbers, or mathematics in general, it is advisable to use "linear algebra" (algebra typeset into a single line, without superscripts or subscripts) or pseudocode.

For example, instead of writing "Corrected mathematical formula to sum of reciprocals of squares of factorials instead of sum of reciprocals of factorials of squares, corrected links to Italian, Chinese Wikipedias", you could write "Corrected formula Sum(1/n!^2) instead of Sum(1/n^2!), corrected it:, zh:"

In edit summaries, use the mathematical operators available on the standard keyboard (+, -, *, /, ^) even though a different operator (e.g., ×) would be more appropriate in the article text.

Although Greek letters can technically be used in edit summaries, it is preferable to use the name of the letter spelled out in the English alphabet. For example, "Changed e to pi in formula", "Mu(100) is 0, not 1" (The article text should of course fully avail itself to any applicable Greek letters).

Some shorthand notations that might be useful:

 n, num, # An arbitrary integer p An arbitrary prime number x, num, # An arbitrary real number val Value tri; sq, ^2; pentag; hexag; heptag, etc. Triangular; square; pentagonal; hexagonal; heptagonal, etc. sum; prod Sum; product !; !!; super!, \$!; hyper!; ¡!, i!; !sum; 1/! Factorial; double factorial; superfactorial; hyperfactorial; alternating factorial; factorial sum; reciprocal of factorial bin; oct; dec; hex Binary; octal; decimal; hexadecimal Infobox, Docuan table The table with binary, hexadecimal representation, factorization and other general data points about the number

### Flagship articles

Articles for the first twelve integers are some of the most well-developed number articles, in terms of mathematical properties and cultural associations, as well as sourcing. This being said, there are many other number articles that are well-written and can serve as examples:

• The articles for 0 and 1, which are elementary numbers in mathematics with many fundamental properties and characterizations. These articles notably have more diverse mathematics sections devoted to highlighting some of their essential properties.
• The article for the number 5 is diverse in ascribing mathematical properties that are both number-theoretical, as well as geometric and algebraic, including many other cultural associations and otherwise (it is also well-cited, with over 170 sources).
• The article for the number 11 contains a good amount of mathematical properties that also include decimal-specific properties (as an example of a common subsection within mathematics that can be expanded within other articles).
• The article for the number 24 has been known to have some of the most complex geometric properties listed among Wikipedia number articles, and has expanded today to include also many other number-theoretical properties.
• The article for the number 73 has plenty of information on a specific connection with the number 37, and is an example of such a focus that bridges with another number (and number article).
• The article for the number 288 contains several note-worthy properties that are highlighted effectively and presented in tandem.
• The article for the number 1729 is an example of an article that highlights one major property, while listing other properties as well under a different subsection. It is also an article about a well-known and culturally important number in mathematics.

## Progress

The following is the status of the project as of January, 2023.

### Priority of mathematics articles

Following the level of priority set by WikiProject Mathematics:

#### Top-priority

There are five top-priority mathematics number articles:

• Integers: -1, 0, and 1.
• Constants: π and e

Currently, articles for 0 and 1 are well-written within their respective mathematics sections, however they are not generally referenced (even though they contain due links, they could use primary sourcing where possible, even when generalizing). The article for π is a featured article, and the article for e is a good article.

#### High-priority

Another ten mathematics number articles are categorized as high-priority:

These have all recently been improved (2022-).

#### Mid-priority

At least four relevant mid-priority mathematical article are listed:

Articles that are listed as low-priority include:

Methodical low-priority assignments to integer number articles have not really taken place, which is something that could be further investigated. For example, 24 (number) could be elevated at least to low-priority, given the many important geometric and algebraic properties assigned to it. 12 is another such candidate.

### Overview

There are continuous individual articles for positive integers from 1 to 263 (with the exception of 198).

• From 260 to 300 there are article pages with information for integers in increments of ten, including very short stubs for non-round numbers in the range 260 to 299, (though a few have their own articles, such as 276 and 284).
• From 300 to 1000 they are grouped by hundreds, including short stubs for some numbers in the range 301 to 999 (some consist of one-liners only), with a few numbers with individual articles such as with 360, 666, and 720.
• From 1000 to 10000, they group in thousands, following the same scheme used for the groups of hundreds; again, some (1001 and 1729 spring to mind) have their own articles.
• From 10000 to 100000 articles grow in increments of ten thousand, with a few articles in between for individual numbers (like 65,536 and 65,537).
• From 105 through 109 articles articles are grouped in ranges of increments of powers of ten (i.e. the largest consecutive 10n article we have is for one billion).
• There are select number articles greater than 109 such as 2,147,483,647 and 4,294,967,295, and even extending to 1012, a googolplex, and Graham's number.

Navigation bars inside Docuan tables of number articles have been created with the follow functionality:

• Increments of 1 for all numbers between 0 and 270 (including redirects back to 260 between 260-269).
• Increments of 10 from 0 through 300 (bugging between 280 and 300, however).
• Increments of 100 from 0 through 1000 (starting at 100), of 1000 between 1000-9000, and of 10000 between 10000-90000.
• Increments by factors of 101 between 100 and 109 (i.e. 100, 101, 102, ... 109 with links starting at 105).

Status of disambiguation pages:

#### Naming compliance

The issue of naming number articles went through a vote. Egil's proposal for naming the articles Number N_(number), and making the spelled out names of the numbers be redirects (e.g., Four hundred and ninety-six redirects to 496 (number)) received the most votes; and with the initiative of Dysprosia, the articles were moved accordingly. The issue of whether the "British" spelling out of numbers or the "American" spelling out should be used remains, but is no longer as pressing as it once was.

Numbers deserving their own article that are greater than 999, should have the article title written in digits without any separators between the digits of the integer part. Writing the number with separators may of course be acknowledged in the body of the article. Thus, the article on the taxicab number should be 1729 (number), though the article can mention that the number may be written "1,729" or "1.729."

Besides -1, there are no articles on negative integers. Adding information about a negative number therefore can fall under articles representative of numbers' positive, absolute values. One half is the chosen article name for 1/2.

### Articles for deletion

#### Current

For up-to-date and automatically updated list of articles for deletion, see Category:AfD debates subsection 0–9.

## Participation

#### Past or inactive members

These members have already done great work on number articles. Asking them to sign up is more than a formality, however. It is to better coordinate the project. If someone could join this project given their past contributions or from a particular voiced interest, please list them here.

• David Eppstein has been involved in math articles.
• MFH hasn't been involved in 'number' articles, but has been active in Math articles, and has an OEIS account.

### Userboxes

Code Result
{{Template:User interest numbers}}
 This user is interested inNumbers.
Usage
{{Template:User WP Numbers}}
 81 This user is a member ofWikiProject Numbers
Usage

Some of the following talk pages include it: What links here

### Talk

To add a message of this project to talk pages of number articles, use Template:NumberTalk that can be displayed with {{WikiProject Numbers}}.

WikiProject Numbers
 This article is within the scope of WikiProject Numbers, a collaborative effort to improve the coverage of Numbers on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.NumbersWikipedia:WikiProject NumbersTemplate:WikiProject NumbersNumbers articles